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上海市进才中学2018-2019学年高二上学期期末数学试题
上海 高二 期末 2019-11-14 133次

一、填空题添加题型下试题

1. 关于eqId502807952f124aa59677e2cf5ed4f275的二元一次方程的增广矩阵为eqId66cdb377604a4ce88c23c6e1ac7ece3d,则eqId8ba2412c62ae4679919615b3361cfed8________。
2. 已知eqId877b36b734604da5a7457a511d3be18f,则eqId3719fcad464c419291c2d254d26e10f2对应的坐标是__________
3. 已知直线eqId924eb00f03d34810a52d51f8e5603a44与直线eqIdfaaf3935b4f84fcd90598035dc8d8f26重合,则eqId783c5f01aa1e49b29f88c27d2eca4354________。
4. 在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId99a3187c2b8f4bcc9703c74c3b72f1f3中点,eqId63db14a5b4334f3ea583c8fb12b0d175eqId0627be51821d4be7b3e024a354815d64中点,则直线eqId3dd88fd134c1472886302db0246dfc44eqIdb35a05fd40df4e45a90c95b6795b74b1的位置关系是__________
7. 经过动直线eqId01b934206c224be087b35f8f2b26fadb上的定点,方向向量为eqId1adb9c9b0e1745f99ef96824a1cd4fa9的直线方程是___________。
9. 过点eqId4b578a55a1504b0ea83516617cedee58且和双曲线eqId293f47bac2574675bc7717ac6dde0f4f有相同的焦点的椭圆方程为____________。
11. 平面上一机器人在行进中始终保持与点eqIda0ef3dd8a1184aafb6117954ed2a40bc 的距离和到直线eqId185bd986038b40399cbf19fc634eeb2d的距离相等,若机器人接触不到过点eqId574032e8cdbe4bea969bd1efd3642d3f且斜率为eqId4d2187284c5d4de29906363f7d21f60f的直线,则eqId4d2187284c5d4de29906363f7d21f60f的取值范围是___________。
12. 已知圆M:eqIde2573299e9394949baa5e3ce96fc5af2,圆N:eqId162ab95be07f4a6aaf7f2b58c7e90b2c直线eqIdef8f264ad2c44dad8a7a514d8f1f4d95分别过圆心M、N,且eqId74c7e0292b094e54ae596d37798a05ed与圆M相交于A,B两点,eqId439fb93f7745417b8bb1747d963c6e60与圆N相交于C,D两点,点P是椭圆eqId91d66d2ff9474de29add2003ee3c1721上任意一点,则eqIda8c57f4afc5442ceb7e12b97bdc292a2的最小值为______.

二、单选题添加题型下试题

15. 将正方体表面正方形的对角线称为面对角线.若eqId9970d680afda4f1eb4ccad4679b30f2d是同一正方体中两条异面的面对角线,则eqId6968eb809c7b4a0ead1a5dd2050f1a50所成的角的所有可以取得的值构成的集合是(   )
A.eqId4f7c116bd81243bbb01a6c1c2b29db28B.eqIdc9802987d0b74512b89c5995e880e221C.eqIdb8cc434c4da24952be24fba3c5620d16D.eqId8b64d478ff704ba19dc5ccd92e17e74b
16. 下列关于复数eqId2cd9e2fe3d6540df9399dbefe49ada54的四个命题中,正确的个数是(   )
(1)若eqIddb152ac4a98d4698b09630f9b173d1ac,则复数eqId2cd9e2fe3d6540df9399dbefe49ada54对应的动点的轨迹是椭圆;
(2)若eqIdcd162f7b288745fdaf5e9d68d918feb2,则复数eqId2cd9e2fe3d6540df9399dbefe49ada54对应的动点的轨迹是双曲线;
(3)若eqIdbb912684c76d49f48c06f3f1b1fb7d6d,则复数eqId2cd9e2fe3d6540df9399dbefe49ada54对应的动点的轨迹是抛物线;
(4)若eqId37d168093dd7462f88523a76949124e8,则eqId0df13435d60b43c598782b0422a17d8c的取值范围是eqId2326546a2b964ad4a2d6814ff66da78b
A.4B.1C.2D.3

三、解答题添加题型下试题

17. 设eqId81565c1c89b742e197b5b860c0258ba2,关于eqId8e15963708e9415da25069fea5906e24的方程eqId2bccf3ca400f40f5afc1226812466dcb的两个根分别是eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159.
(1)当eqId2618daf261754a37930b0c624e147f20时,求eqId4eb56f42ca674f2f9c9101b548763159eqId81599c3323674e779a26dbc74696c051的值;
(2)当eqIdb9614a3e6e704030ae90736c9369ca48时,求eqIdf6a970b082f445f5903eafebf24e442f的值.
18. 过抛物线eqIdd050af449075401299cc78c647d310e8的焦点eqIdd5b10b2a13f148b78e0d5a1b820538fd的直线交抛物线于点eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c(其中点eqIdcc614bd3390c4d028df189b234dcc351在第一象限),交其准线eqId417e80f1349244878d01fe90e0891f5f于点eqId19a4eb16029e4550a14f2afe4741a3c3,同时点eqIdd5b10b2a13f148b78e0d5a1b820538fdeqIdcf2da96900c948a1b3ce7cbfd420c080的中点.
(1)求直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3的倾斜角;
(2)求线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的长.
19. 已知eqId2381423d4cd146cab95f55527681a766为圆eqId2efda802d5534f6d92d9f8af7aaec28beqId7a74452793a34aa0816c74e93747ed60上的动点,过点eqId2381423d4cd146cab95f55527681a766eqId8e15963708e9415da25069fea5906e24轴、eqId072d7d6b911b42bc89207e72515ebf5f轴的垂线,垂足分别为eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,连接eqIde04edefc56124dc78f4e0df9bc1e5373延长至点eqIdbedf755e0fdb4d078d6859360706b163,使得eqId572c3e0bd2264b029942c37592cb9653 ,记点eqIdbedf755e0fdb4d078d6859360706b163的轨迹为曲线eqId19a4eb16029e4550a14f2afe4741a3c3.
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)直线eqId74c7e0292b094e54ae596d37798a05edeqId4610b8c449bb4c1ea8495b323539e6bc与圆eqId2efda802d5534f6d92d9f8af7aaec28b相切,直线eqId439fb93f7745417b8bb1747d963c6e60eqIde9f5f9876a9145e1a2942a042b442ba2与曲线eqId19a4eb16029e4550a14f2afe4741a3c3相切,求eqId96c531282cc34de99017bd2a527f8ec8的取值范围.
典型
20. 已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId15bfbddeee0143e08c809ecf76ffb129,若四点eqId4e6eb3a2e0ee4476bb25dd206f578e52,eqIddf5e330b6db349f4adcc5f1fe1e6e39deqId8e4400ea6bc7425d9a3a78f83b6ccbe1中恰有三点在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上.
(1)指出四点eqId5e100c80e7f84ac9a38ba9d3e8605432中,可能不在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上的点,并说明理由;同时求出椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)过椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的右焦点eqIdd5b10b2a13f148b78e0d5a1b820538fd的直线eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdd43a22caaa934788a99015ca21c61583两点,点eqId2381423d4cd146cab95f55527681a766的坐标为eqId01b73d84e7264262897ad954d2e29050 。设eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,证明:eqIdfa66b499aca94d12b18e1bd344f98546.
典型
21. 双曲线eqIdbf31c16f10784d76851cf83e57c2eeedeqIdc1cf550c5ec946038d5d35812a7c7cae
(1)已知双曲线eqIdbf31c16f10784d76851cf83e57c2eeed的实轴长为eqIdddd35c5d043e4ebeac32a99367053c68,渐近线方程为eqId4114d054e35047019c8724c257b68f5b.求双曲线eqIdbf31c16f10784d76851cf83e57c2eeed的标准方程;
(2)若双曲线eqIdbf31c16f10784d76851cf83e57c2eeed与直线eqIde0134976f9634f1cb9fd2c167faa7c1f交于eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811两点,且eqIdadcf8a0e659b4f77b1ec838722235402 (eqId2efda802d5534f6d92d9f8af7aaec28b为原点),求证:行列式eqId2b252ede9e0e4c4b826fd24fc81085e3的值为常数;
(3)可以证明:函数eqId9a5b4e08a3a343fa9e94ceffbc76d552的图像是由双曲线eqId1a4dae01e22d40a7a773045ec22575c4的图像逆时针旋转eqIdd01b7918993a412cb774dea127f210b6得到的.用类似的方法可以得出:函数eqId6e377689dd7d44fd86300d0b7a98c113的图像也是双曲线.按教材对双曲线的性质的研究,请列出双曲线eqId6e377689dd7d44fd86300d0b7a98c113的性质(不必证明).